Imaging radar system having a receiving array for determining the angle of objects in two dimensions by means of a spread arrangement of the receiving antennas in one dimension

ABSTRACT

The present invention relates to an apparatus for determining the position of objects in two-dimensional space having a first dimension and a second dimension, the direction vector of which is orthogonal to the direction vector of the first dimension, containing at least one transmitter (I) having at least one transmitting antenna ( 3 ) and an imaging receiver circuit ( 2 ) having at least one receiving antenna array (Rx Array) with rows ( 6 ) of receiving antennas for scanning the first dimension by means of digital beam shaping, wherein the receiving antenna array has a linear array, a sparse array or an array with an enlarged aperture, and wherein the rows ( 6 ) of receiving antennas in the receiving antenna array of the receiver circuit ( 2 ) are linearly arranged in the first dimension according to a curve function or according to the contour of a two-dimensional geometric object and are spread out in the second dimension, and to a method using the apparatus.

TECHNICAL FIELD

The present invention relates to a device for determining the positionof objects in two-dimensional space having a first dimension and asecond dimension, the direction vector of which is orthogonal to thedirection vector of the first dimension, comprising at least onetransmitter having at least one transmitting antenna and an imagingreceiver circuit having at least one receiving antenna array (Rx Array)having rows of receiving antennas for scanning the first dimension bymeans of digital beamforming.

Diverse methods of beam sweeping are currently in use in imaging radarsensor technology for automotive applications, which methods can besubdivided into three categories. They are analogue beamforming by meansof a mechanical movement of the antenna, beam sweeping using analoguephase shifters, and digital beam sweeping using the principle of“digital beamforming”. In this case, at least one transmitting channeland a plurality of receiving channels are required and the antenna lobeis shaped by means of phase shifts of the digitized reception signals.This technique reduces the hardware outlay in the radio-frequencyfrontend to a minimum and at the same time increases the reliability andflexibility of the systems. Moreover, planar antennas can be used, whichpermits a compact and cost-effective design of the sensors.

PRIOR ART

The use of one-dimensional digital beamforming has become established inautomotive radar sensors. Disadvantageously, however, this techniquedoes not allow conclusions to be drawn about the position of an objectin two-dimensional space, but rather only a location determination inone dimension.

DE 10 2011 113 018 A1 describes the use of a plurality of transmittingchannels, wherein, by means of MIMO-on-TX, the aperture is syntheticallyenlarged and allows the sweep angle to be increased. Furthermore,diverse methods exist for determining the position of an object intwo-dimensional space, each of these methods having individual strengthsand weaknesses.

Use of a fully filled two-dimensional array makes it possible to apply abeamformer over the individual rows and columns and thus to enable thetwo-dimensional location determination by means of a CFAR algorithm. Thearchitecture provides for a high suppression of the sidelobes andreduces the occurrence of false alarms. The disadvantage of thisarchitecture arises from the complex construction thereof, whichconsiderably limits usability in automotive applications. The primaryfield of use of such architectures is found principally in militaryapplications. Besides densely filled arrays, so-called “sparse arrays”are also used, in which rows of antennas in the two-dimensionalreceiving array are deliberately omitted. In this implementation, therouting outlay is significantly reduced at the expense of reducedsidelobe suppression. Furthermore, use is made of less complexarchitectures with a so-called amplitude monopulse. The two-dimensionalbeamforming arises from two transmitting antennas and a receiving array,wherein the transmitting antennas have a tilted antenna pattern withrespect to one another. The location determination in the seconddimension then results from the antenna patterns and also the amplitudecomparison of the reception signals. This method has the disadvantage,however, that it requires complex, individual calibration of the radarsensors since in some instances severe distortions of the directivitypatterns of the antennas can occur as a result of the type ofinstallation position and covering in an automobile.

This problem is avoided with the use of a phase monopulse, cf. DE 102014 014 864 A1. The architecture here is constructed analogously to thearchitecture in the case of an amplitude monopulse. Rather than theamplitude, however, the phase difference between the reception signalsof the two virtual receiving arrays is evaluated in the signalprocessing. In addition to the methods described above, it isfurthermore possible to implement a location determination on the basisof a known beam characteristic of Tx and/or Rx antennas.

Disadvantageously here use is made of one or alternatively a pluralityof transmitting antennas and also a plurality of receiving antennaarrays each having a plurality of rows of receiving antennas whichresults in a considerable space requirement and routing outlay and, notleast, crucially influences the costs of the system. Therefore, it isdesirable to minimize the number of rows of receiving antennas withoutlosses in functionality.

DESCRIPTION OF THE INVENTION

Therefore, the problem addressed by the present invention is that ofproviding an improved device and method for the non-contactdetermination of the position of one or more objects in space by meansof an imaging radar sensor using digital beamforming.

This problem is solved according to the invention by means of a deviceas claimed in claim 1 and a method as claimed in claim 11.

The basic concept of the present invention is that the receiving antennaarray has a linear array, a sparse array or an array with an enlargedaperture, wherein the rows of receiving antennas of the receivingantenna array of the receiver circuit are arranged linearly in the firstdimension in accordance with a curve function or in accordance with thecontour of a two-dimensional geometric object and are spread out in thesecond dimension.

The invention is distinguished here by the fact that it is possible tocarry out digital beamforming for determining the location of objects inconjunction with small sidelobes in both dimensions. Said smallsidelobes make it possible to ensure a low false alarm rate in theapplication.

Particularly advantageously here use is made of a receiving antennaarray arrangement that is arranged linearly in the first dimension insuch a way that a second transmitting antenna or alternatively a secondreceiving antenna array is not necessarily required for locationdetermination in the second dimension. The field of use of themillimeter-wave radar sensor described is principally focused onautomotive applications, resulting in requirements made of the sensorwhich concern, inter alia, the sensor's size, distance and angleresolution in azimuth and elevation and also the necessary update rateand thus the maximum duration of an individual measurement. At the sametime, a high reliability is made possible since the sensor system mustbe able to identify obstacles without delay and to make available to theautomobile relevant data such as the position and extent of saidobstacles. Advantageously here use is made of one or alternatively aplurality of transmitting antennas and also a plurality of receivingantenna arrays each having a plurality of rows of receiving antennaswhich results in a considerable space requirement and routing outlayand, not least, crucially influences the costs of the system. Therefore,the aim is to minimize the number of rows of receiving antennas withoutlosses in functionality.

Preferably, the rows of receiving antennas of the receiver circuit arearranged as a straight line, triangle, sawtooth, or sinusoidally in thefirst dimension. Alternatively, the rows of receiving antennas of thereceiver circuit are arranged as a rectangle, circle, or ellipse in thefirst dimension.

Advantageously, the receiving antenna array (Rx-Array) described is alinear array, a sparse array, or an array of large aperture andarbitrarily positioned antennas. In this case, the arrangement of theindividual rows of receiving antennas is effected with the aid of anarbitrary curve function, e.g. a straight line, a triangle, a sawtooth,a sine function, or alternatively on the open or closed contour of anarbitrary two-dimensional geometric object, such as e.g. a rectangle, atriangle (with an open contour: V-shape), a circle (with an opencontour: circle arc) or an ellipse, wherein in each case the orientationof the first and second dimensions is predefined and the array is spreadout in the second dimension. As a result of the array being spread outin a second dimension, the array described makes it possible, without afurther receiving antenna array, simultaneously to obtain informationabout the positioning of the object in two-dimensional space inconjunction with small sidelobes.

Preferably, the phase centers of the rows of receiving antennas of thereceiver circuit are arranged in a non-regular pattern in the seconddimension.

The rows of receiving antennas are thus spread out in a non-regularpattern and the number of different discrete positions in the seconddimension of the rows of receiving antennas (6) N_(Pos,2D) is at leastthree, but preferably N_(Pos,2D)≥√{square root over (N_(RxANT))}, thenumber of rows of receiving antennas used overall being given byN_(RxANT). In order to simplify the positioning, a random function canbe used, the spacing of the maximum deviation from the mean value in thesecond dimension being predefined.

Preferably, the real receiving antenna array (Rx ANT) of the receivercircuit is able to be enlarged by at least two switchable transmittingantennas by means of MIMO-on-Tx to form a virtual receiving antennaarray (Rx Virt) having a number of virtual elementsN_(RxVirt)>N_(RxANT).

In this case, in the second dimension the phase centers of thetransmitting antennas are identical, or, additionally or alternatively,in the second dimension the phase centers of the transmitting antennasare different and an additional offset is formed in the virtualreceiving antenna array (Rx Virt) as a result.

Consequently, the device can be used not only for radar systems with onetransmitter and a single transmitting antenna, but advantageously alsoin radar systems with so-called MIMO-on-TX. The latter denotes theextension of a real receiving array to form a virtual array by the useof at least two or more switchable transmitting antennas. The number ofvirtual elements N_(RxVirt)>N_(RxANT) results from the arrangement ofthe transmitting antennas with respect to the receiving channels.Various possibilities for the arrangement of the transmitting antennasarise here. Firstly, the transmitting antennas can be arranged in such away that in the second dimension they have no offset with respect to oneanother and accordingly do not cause additional spreading of the virtualreceiving array. Alternatively or additionally, however, it is alsopossible to utilize further transmitting antennas actively foradditional spreading of the receiving array by means of an offset in thesecond dimension. By means of various signal processing methods, animprovement of the beamforming in at least one direction can be achievedfor both embodiments of the device as hardware variants.

The receiving antenna array of the receiver circuit is thus enlargedusing at least two switchable transmitting antennas by means ofMIMO-on-Tx to form a virtual array having a number of virtual elementsN_(RxVirt)>N_(RxANT), in particular with identical phase centers of thetransmitting antennas in the second dimension, or with different phasecenters of the transmitting antennas in the second dimension, with theresult that an additional offset is generated in the virtual receivingarray, or, under the assumption of more than two transmitting antennas,by means of a combination of both variants.

Besides an improvement of the focusing in the first dimension, i.e. anarrower antenna lobe in the main beam direction, what is also achieved,as a result of the aperture being enlarged, is an improvement of thegrating lobes by means of the switching of the transmitting antennasusing half-row SAR.

An improvement in the second dimension results from the fact thatadditional spreading is achieved as a result of an offset of thetransmitting antennas in the second dimension and the beamforming inthis dimension thus leads to a narrower lobe. A higher number oftransmitting antennas with at the same time an offset in the seconddimension can thus result in an improvement of the characteristics inboth dimensions.

Preferably, the device described is suitable for use in afrequency-modulated CW radar method, in digitally modulated radar and/orin a pulse radar.

Preferably, the number of rows of receiving antennas is N_(RxANT)≥4.

Preferably, the at least one transmitting antenna and the imagingreceiver circuit are operable in the frequency range of 1 GHz to 300GHz, preferably in the frequency range of 20 GHz to 160 GHz,particularly preferably in the frequency range of 76 GHz to 81 GHz.

The effectiveness of the improvements to be achieved by the spreading ofthe receiving antennas is therefore independent of the basic form andlikewise independent of the radar method used. On account of the fieldof use in automotive radar applications, the described device and alsothe method are primarily provided for the frequency band of 76-81 GHz,but are not limited to this frequency range. Fundamental usability isafforded in the complete centimeter- and millimeter-wave range in therange of 1 GHz to 300 GHz, but is not restricted to a concretizedfrequency range.

The method according to the invention for determining the position ofobjects in two-dimensional space having a first dimension and a seconddimension, using the device described, comprises the following steps:

-   -   transmitting a radar signal by means of at least one        transmitting antenna;    -   receiving a signal by means of an imaging receiver circuit        having at least one receiving antenna array (Rx Array) for        scanning the first dimension;    -   digitizing the signal data;    -   carrying out a range FFT and/or a velocity FFT and digital        beamforming;    -   object detection and position determination.

The signal processing, underlying the method, for calculating thetwo-dimensional target position is illustrated in FIG. 4 in the form ofa signal flow diagram for the example of an FMCW radar. After themeasurement, that is to say the transmission, reception and digitizationof a ramp, the basis for the subsequent digital beamforming is firstlyestablished by means of a range FFT and a velocity FFT. The targetdetection is carried out firstly in the first dimension, e.g. by meansof an OSCFAR or a Peak search function, followed by beamforming in thesecond dimension on the basis of the FFT data at the positions of thetargets previously found in the first dimension. The further positiondetermination in the second dimension is carried out as described below.Finally, the two-dimensional data of the so-called range-velo cells arecalculated from the combination of both beamformers.

Preferably, the object detection is carried out in the first dimensionand the position determination is carried out in the second dimension.

The target detection in the second dimension is carried out by digitalbeamforming over the elements distributed irregularly in this dimension,wherein the lobe width attained is substantially defined by the standarddeviation of the random distribution. In addition, moreover, anamplitude monopulse can be employed.

Preferably, upon successful object detection in the first dimension, theposition determination is subsequently carried out with beamforming fora plurality of beams in the second dimension.

Preferably, upon successful object detection in the first dimension, theposition determination is subsequently carried out with beamforming andan amplitude monopulse for a plurality of beams in the second dimension.

Preferably, when the rows of receiving antennas of the receiving antennaarray are arranged in accordance with a curve function, the positiondetermination is subsequently carried out with 2D beamforming on thebasis of the phase centers.

One embodiment of the device and of the method is explained in greaterdetail below with reference to the drawing, without any desire for theinvention thereby to be restricted.

In the embodiment described, the arrangement can be described by meansof a Cartesian coordinate system; the direction vectors of the twodimensions are orthogonal to one another.

In the figures:

FIG. 1 shows a front end having 16 Rx antennas and one Tx antenna.Arrangement of the Rx antennas in the 2^(nd) dimension by rand( )*Max.deviation;

FIG. 2 shows an antenna pattern in the 2^(nd) dimension with threeshaped beams by virtue of different positionings of the phase center inthe 2^(nd) dimension;

FIG. 3 shows an antenna pattern in the first dimension for the antennapositions listed in table 1 (1^(st) dim. linear, 2^(nd) dimensionrandomly generated) and for a linear array of the antenna positionswithout a deviation in the second dimension;

FIG. 4 shows a signal flow diagram of the 2D location determination withthe use of FMCW; and

FIG. 5 shows an elliptic array arrangement having 2 Tx and 8 Rx.

FIG. 1 shows such an exemplary implementation of a radar front endconsisting of a transmitter (1) having a transmitting antenna (3) and areceiver circuit (2) having 16 rows of receiving antennas (6), whereinthe rows of receiving antennas (6) are oriented linearly on a straightline along the first dimension. The array is spread out in the seconddimension, which is orthogonal to the first dimension, with the aid of arandom function. The associated positions of the linear array having therow spacing 2200 μm in the first dimension and randomly determinedpositions in the second dimension are presented in table 1:

TABLE 1 Positioning of the rows of receiving antennas of the arrayillustrated in FIG. 1 with a linear arrangement in dimension 1 with arow spacing of 2200 μm and a randomly produced arrangement of theantennas in dimension 2. Dim 1 (μm) Dim 2 (μm) −1260    0 R × 1 −1620  2200 R × 2 1490   4400 R × 3 −1650   6600 R × 4 −530   8800 R × 5 161011 000 R × 6 890 13 200 R × 7 −190 15 400 R × 8 −1830 17 600 R × 9 −186019 800 R × 10 1370 22 000 R × 11 −1880 24 200 R × 12 −1830 26 400 R × 1360 28 600 R × 14 −1200 30 800 R × 15 1430 33 000 R × 16

FIG. 2 shows three resulting beams in the second dimension for the frontend having one transmitter and 16 receiving channels as illustrated inFIG. 1 . In this case, the spreading of the position of the phase centerresults in an angle offset of the viewing direction of the beams andthus also allows an evaluation in the second dimension. In this case,the maximum deviation of the spreading from the mean value must bedefined in such a way that for a finite number of receiving rows, thebeamforming in the first dimension is not critically influenced.

FIG. 3 shows by way of example the antenna pattern produced by digitalbeamforming for a main beam direction of 0° in a comparison between alinear array without and with a spread-out second dimension. It isevident here that the effects of the spreading in the second dimensionare manifested only marginally in the antenna pattern, principally atthe sidelobes.

FIG. 4 shows the signal processing for calculating the two-dimensionaltarget position in the form of a signal flow diagram on the basis of theexample of an FMCW radar. After the measurement, that is to say thetransmission, reception and digitization of a ramp, the basis for thesubsequent digital beamforming is firstly established by means of arange FFT and a velocity FFT. The target detection is carried outfirstly in the first dimension, e.g. by means of an OSCFAR or a Peaksearch function, followed by beamforming in the second dimension on thebasis of the FFT data at the positions of the targets previously foundin the first dimension. The further position determination in the seconddimension is carried out as described above. Finally, thetwo-dimensional data of the so-called range-velo cells are calculatedfrom the combination of both beamformers.

FIG. 5 illustrates an exemplary arrangement of a MIMO-on-TX radar systembased on an elliptic arrangement of the antennas. In the arrangementshown, the phase centers of the eight rows of receiving antennas (6) lieon the contour of the ellipse described by the angle-dependent radius rthereof:

${{r(\partial)}^{2} = \frac{a^{2}b^{2}}{{a^{2}{\sin(\partial)}} + {b^{2}{\cos(\partial)}}}},$

wherein the maximum radius is defined by a and the minimum radius of theellipse is defined by b. In the arrangement shown, here the radius formsthe first dimension, the random distribution being applied to the angle,which accordingly represents the second dimension. The MIMO-on-TX ismade possible by means of two switchable transmitting antennas (3),which are positioned in different positions relative to the ellipse.

Reference Signs

1 Transmitter

2 Receiver circuit

3 Transmitting antenna

4 Phase center

5 Row spacing

6 Row of receiving antennas

7 Viewing direction (deviation 1)

8 Directivity characteristic dim. 2 (deviation 1)

9 Viewing direction (deviation 2)

10 Directivity characteristic dim. 2 (deviation 2)

11 Viewing direction (deviation 3)

12 Directivity characteristic dim. 2 (deviation 3)

13 Sidelobes

1-15. (canceled)
 16. A radar system comprising: a transmitter antenna; afirst row of receiver antennas, where the first row of receiver antennashas a first phase center at a first position along the first row ofreceiver antennas; a second row of receiver antennas, where the secondrow of receiver antennas has a second phase center at a second positionalong the second row of receiver antennas, where the first row ofreceiver antennas is offset from the second row of receiver antennas ina first dimension, where the first row of receiver antennas and thesecond row of receiver antennas extend in parallel with one anotheralong a second dimension, and further where the first position of thefirst phase center is offset from the second position of the secondphase center in the second dimension; and processing circuitry that isin communication with the first antennas and the second antennas, wherethe processing circuitry is configured to perform acts comprising:obtaining a first signal from the first row of receiver antennas, wherethe first signal is based upon a radar signal emitted into anenvironment by the transmitter antenna, and further where theenvironment includes an object; obtaining a second signal from thesecond row of receiver antennas, where the second signal is based uponthe radar signal emitted into the environment by the transmitterantenna; digitizing the first signal and the second signal to form firstdigitized data and second digitized data, respectively; performingdigital beamforming based upon the first digitized data and the seconddigitized data; and computing a position of the object in theenvironment in both azimuth and elevation.
 17. The radar system of claim16, further comprising a third row of receiver antennas that has a thirdphase center that has a third position along the third row of receiverantennas, where the third row of receiver antennas is offset from boththe first row of receiver antennas and the second row of receiverantennas in the first dimension, where the third row of receiverantennas extends in parallel with the first row of receiver antennas andthe second row of receiver antennas along the second dimension, andfurther where third position of the third phase center is offset fromthe first position of the first phase center and the second position ofthe second phase center in the second dimension; wherein the actsperformed by the processing circuitry further comprise: obtaining athird signal from the third row of receiver antennas, where the thirdsignal is based upon the radar signal emitted into the environment bythe transmitter antenna; and digitizing the third signal to form thirddigitized data, wherein the digital beamforming is performed basedfurther upon the third digitized data.
 18. The radar system of claim 16comprising eight rows of receiver antennas, where the eight rows ofreceiver antennas include the first row of receiver antennas and thesecond row of receiver antennas, and further where the digitalbeamforming is performed based upon signals obtained from the eight rowsof receiver antennas.
 19. The radar system of claim 16 comprisingsixteen rows of receiver antennas, where the sixteen rows of receiverantennas include the first row of receiver antennas and the second rowof receiver antennas, and further where the digital beamforming isperformed based upon signals obtained from the eight rows of receiverantennas.
 20. The radar system of claim 16, where the first row ofreceiver antennas includes first planar antennas coupled to one anotherin series, and further where the second row of receiver antennasincludes second planar antennas coupled to one another in series. 21.The radar system of claim 16 mounted on an automobile.
 22. The radarsystem of claim 16, further comprising a row of transmitter antennasthat extend in the second dimension in parallel with the first row ofreceiver antennas and the second row of receiver antennas, where the rowof transmitter antennas is offset from the first row of receiverantennas and the second row of receiver antennas in the first dimension,and further where the row of transmitter antennas includes thetransmitter antenna.
 23. The radar system of claim 16, wherein a randomfunction is employed to set the first position and the second position.24. The radar system of claim 16, further comprising a secondtransmitter antenna that is offset from the transmitter antenna in thesecond dimension, where the transmitter antenna and the secondtransmitter antenna are switchable.
 25. The radar system of claim 16being a pulse radar system.
 26. The radar system of claim 16, where thefirst dimension is orthogonal to the second dimension.
 27. The radarsystem of claim 16, where the first row of receiver antennas and thesecond row of receiver antennas are oriented linearly on a straight linein the first dimension.
 28. The radar system of claim 16, where adistance between the first row of receiver antennas and the second rowof receiver antennas along the first dimension is 2200 μm.
 29. A methodfor forming a radar system, the method comprising: providing atransmitter, where the transmitter includes a transmitter antenna;providing a receiver circuit, where the receiver circuit comprises: afirst row of receiver antennas, where the first row of receiver antennashas a first phase center at a first position along the first row ofreceiver antennas; a second row of receiver antennas, where the secondrow of receiver antennas, where the second row of receiver antennas hasa second phase center at a second position along the second row ofreceiver antennas, where the first row of receiver antennas is offsetfrom the second row of receiver antennas in a first dimension, where thefirst row of receiver antennas and the second row of receiver antennasextend in parallel with one another along a second dimension, andfurther where the first position of the first phase center is offsetfrom the second position of the second phase center in the seconddimension; operably coupling processing circuitry to the receivercircuitry; and programming the processing circuitry to perform actscomprising: obtaining a first signal from the first row of receiverantennas, where the first signal is based upon a radar signal emittedinto an environment by the transmitter antenna, and further where theenvironment includes an object; obtaining a second signal from thesecond row of receiver antennas, where the second signal is based uponthe radar signal emitted into the environment by the transmitterantenna; digitizing the first signal and the second signal to form firstdigitized data and second digitized data, respectively; performingdigital beamforming based upon the first digitized data and the seconddigitized data; and computing a position of the object in theenvironment in both azimuth and elevation.
 30. The method of claim 29,wherein the acts further comprise: prior to performing the digitalbeamforming, performing a range Fast Fourier Transform (FFT) and avelocity FFT with respect to the first digitized data and the seconddigitized data.
 31. The method of claim 30, wherein the acts furthercomprise: employing a peak search function over frequencies in signalsgenerated based upon the range FFT and the velocity FFT.
 32. The methodof claim 29, wherein the receiver circuit further comprises: a third rowof receiver antennas that has a third phase center that has a thirdposition along the third row of receiver antennas, where the third rowof receiver antennas is offset from both the first row of receiverantennas and the second row of receiver antennas in the first dimension,where the third row of receiver antennas extends in parallel with thefirst row of receiver antennas and the second row of receiver antennasalong the second dimension, and further where third position of thethird phase center is offset from the first position of the first phasecenter and the second position of the second phase center in the seconddimension; where the acts further comprise: obtaining a third signalfrom the third row of receiver antennas, where the third signal is basedupon the radar signal emitted into the environment by the transmitterantenna; and digitizing the third signal to form third digitized data,wherein the digital beamforming is performed based further upon thethird digitized data.
 33. The method of claim 29, where the first row ofreceiver antennas includes first antennas and the second row of receiverantennas includes second antennas, the method further comprising: priorto providing the receiver circuit: utilizing a random function todetermine positions of the first antennas in the first row of receiverantennas; and utilizing the random function to determine positions ofthe second antennas in the second row of receiver antennas.
 34. Themethod of claim 29, wherein the radar system is a pulse radar system.35. A method performed by a radar system to compute a position of anobject in an environment, the method comprising: obtaining a firstsignal from a first row of receiver antennas of the radar system, wherethe first signal is based upon a radar signal emitted into anenvironment by a transmitter antenna of the radar system, where theenvironment includes an object, and further where the first row ofreceiver antennas has a first phase center at a first position along thefirst row of receiver antennas; obtaining a second signal from a secondrow of receiver antennas of the radar system, where the second signal isbased upon the radar signal emitted into the environment by thetransmitter antenna, where the second row of receiver antennas has asecond phase center at a second position along the second row ofreceiver antennas, where the first row of receiver antennas is offsetfrom the second row of receiver antennas in a first dimension, where thefirst row of receiver antennas and the second row of receiver antennasextend in parallel with one another along a second dimension, andfurther where the first position of the first phase center is offsetfrom the second position of the second phase center in the seconddimension; digitizing the first signal and the second signal to formfirst digitized data and second digitized data, respectively; performingdigital beamforming based upon the first digitized data and the seconddigitized data; and computing a position of the object in theenvironment in both azimuth and elevation.